Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 6, Problem 29E
a)
To determine
To draw the model which shows 68-95-99.7
a)
Expert Solution
Explanation of Solution
Given:
μ = 10.4
σ = 4.7
Following is the model which shows 68-95-99.7:
b)
To determine
To explain what size to be expected that central 95% of all trees.
b)
Expert Solution
Answer to Problem 29E
An interval in which central 95% of trees to be found between 1 and 19.8
Explanation of Solution
Given:
μ = 10.4
σ = 4.7
According to rule of 68-95-99.7, the 95% of the values are within 2 standard deviation of the
Therefore,
μ−2σ=10.4−2×4.7=1μ+2σ=10.4+2×4.7=19.8
Hence, interval in which central 95% of trees to be found between 1 and 19.8
c)
To determine
To find the percentage of trees that should be less than 1 inch in diameter.
c)
Expert Solution
Answer to Problem 29E
The 2.5% of the trees are less than an inch in diameter.
Explanation of Solution
Given:
μ = 10.4
σ = 4.7
According to rule of 68-95-99.7, the 95% of the values are within 2 standard deviation of the mean.
Therefore,
μ−2σ=10.4−2×4.7=1μ+2σ=10.4+2×4.7=19.8
That means, 1 inch is two standard deviations from the mean. According to rule, 95% of the data lies between 2 standard deviations from the mean. Since, total data is 100%, so 5% of the data is the more than 2 standard deviations from the mean. Therefore, as per symmetry, 2.5% is more than 2 standard deviations below the mean and 2.5% is more than 2 standard deviations above the mean.
Hence, approximately 2.5% of the trees are less than an inch in diameter.
d)
To determine
To find the percentage of trees that should be between 5.7 and 10.4 in diameter.
d)
Expert Solution
Answer to Problem 29E
The 32% of the trees are between 5.7 and 10.4 an inch in diameter.
Explanation of Solution
Given:
μ = 10.4
σ = 4.7
According to rule of 68-95-99.7, the 68% of the values are within 1 standard deviation of the mean.
Therefore,
μ−σ=10.4−4.7=5.7
That means, 5.7 is one standard deviation below the mean.
Therefore, 100%-68% = 32% which is more than mean and less than 1 standard deviation of the mean. Therefore, 32% of the data lie between 5.7 and 10.4
e)
To determine
To find the percentage of trees that should be over 15 in diameter.
e)
Expert Solution
Answer to Problem 29E
The 2.5% of the trees should over 15 inches in diameter.
Explanation of Solution
Given:
μ = 10.4
σ = 4.7
According to rule of 68-95-99.7, 15 is 2 standard deviation from the mean.
According to rule, 95% of the data lies between 2 standard deviations from the mean. Since, total data is 100%, so 5% of the data is the more than 2 standard deviations from the mean. Therefore, as per symmetry, 2.5% is more than 2 standard deviations below the mean and 2.5% is more than 2 standard deviations above the mean.
Hence, 2.5% of the trees should over 15 inches in diameter.
Chapter 6 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Ch. 6 - Prob. 1ECh. 6 - Prob. 2ECh. 6 - Prob. 3ECh. 6 - Prob. 4ECh. 6 - Prob. 5ECh. 6 - Prob. 6ECh. 6 - Prob. 7ECh. 6 - Prob. 8ECh. 6 - Prob. 9ECh. 6 - Prob. 10E
Ch. 6 - Prob. 11ECh. 6 - Prob. 12ECh. 6 - Prob. 13ECh. 6 - Prob. 14ECh. 6 - Prob. 15ECh. 6 - Prob. 16ECh. 6 - Prob. 17ECh. 6 - Prob. 18ECh. 6 - Prob. 19ECh. 6 - Prob. 20ECh. 6 - Prob. 21ECh. 6 - Prob. 22ECh. 6 - Prob. 23ECh. 6 - Prob. 24ECh. 6 - Prob. 25ECh. 6 - Prob. 26ECh. 6 - Prob. 27ECh. 6 - Prob. 28ECh. 6 - Prob. 29ECh. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - Prob. 32ECh. 6 - Prob. 33ECh. 6 - Prob. 34ECh. 6 - Prob. 35ECh. 6 - Prob. 36ECh. 6 - Prob. 37ECh. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Prob. 40ECh. 6 - Prob. 41ECh. 6 - Prob. 42ECh. 6 - Prob. 43ECh. 6 - Prob. 44ECh. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Prob. 47ECh. 6 - Prob. 48E
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